# What is the vertex of y= −4x^2 -7x + 1 ?

May 23, 2017

From vertex form, the vertex is at $\left(- \frac{7}{8} , \frac{65}{16}\right)$, which can be written as $\left(- .875 , 4.0625\right)$

#### Explanation:

$y = - 4 {x}^{2} - 7 x + 1$

Factor out the $- 4$
$y = - 4 \left[{x}^{2} + \frac{7}{4} x - \frac{1}{4}\right]$

$y = - 4 \left[{\left(x + \frac{7}{8} x\right)}^{2} - \frac{49}{64} - \frac{1}{4}\right]$

$y = - 4 \left[{\left(x + \frac{7}{8} x\right)}^{2} - \frac{49 + 16}{64}\right]$

$y = - 4 \left[{\left(x + \frac{7}{8}\right)}^{2} - \frac{65}{64}\right]$

$y = - 4 {\left(x + \frac{7}{8}\right)}^{2} + \frac{65}{16}$

From vertex form, the vertex is at $\left(- \frac{7}{8} , \frac{65}{16}\right)$, which can be written as $\left(- .875 , 4.0625\right)$